Low-Coherence Interferometry: OCT Axial Resolution

Source Spectrum

Center wavelength λ₀ 1050 nm

Spectral bandwidth Δλ 60 nm

Sample

Layer separation Δd 15 μm

Reference Mirror

Mirror depth z_ref 20.0 μm

Coherence Gating

Coherence length L꜀

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Axial resolution Δz

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Signal I(z_ref)

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Δd / Δz ratio

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Two layers resolved? —

How it works

In time-domain OCT a broadband ("low-coherence") source feeds a Michelson interferometer. Two beams reflect back — one from a scanning reference mirror, one from reflective layers inside the sample — and recombine at the detector. Interference fringes appear only while the two path lengths match to within the source's coherence length; this is coherence gating, and it is what lets OCT pick out a single depth without any lens focusing on it.

Coherence length:   L_c = 0.44 · λ₀² / Δλ
Axial resolution:   Δz  = L_c / 2   (round trip)
A-scan envelope:     I(z) = Σᵢ Rᵢ · exp[ -4ln2 · (2(z - dᵢ)/L_c)² ]

Each sample layer i sits at depth d_i with reflectivity R_i; the round-trip path mismatch to the reference mirror is 2(z − d_i). The exponential is the Gaussian coherence function that follows from a Gaussian source spectrum (Wiener–Khinchin theorem) — its FWHM is exactly L_c. The displayed A-scan is this envelope after demodulation, exactly what a real OCT system shows (the underlying optical fringe oscillates at λ₀, far too fast to plot at micron depth scale).

λ₀, Δλ — center wavelength and bandwidth of the source. A wider Δλ gives a shorter coherence length and finer axial resolution: this is the core OCT resolution/bandwidth trade-off.
Layer separation Δd — distance between the two sample reflectors. When Δz (resolution) is larger than Δd, their two coherence-gated peaks merge into one — the two layers can no longer be told apart.
Mirror depth z_ref — where the reference arm is currently path-matched; the detector only lights up brightly when a sample layer sits within about one coherence length of this depth. Auto-Scan sweeps it to build the full A-scan.

Real systems (SD-OCT retinal scanners, anterior-segment imagers) use superluminescent diodes with Δλ ≈ 50–100 nm at λ₀ ≈ 840–1310 nm to reach 3–15 μm axial resolution — the same numbers this simulator computes.

Reference arm Sample arm Detector signal

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